Exam C-3 Advanced Surveying 2017 10 1 of 4 CANADIAN BOARD OF EXAMINERS FOR PROFESSIONAL SURVEYORS
C-3 ADVANCED SURVEYING October 2017
Although programmable calculators may be used, candidates must show all formulae used, the substitution of values into them, and any intermediate values to 2 more significant figures than warranted for the answer. Otherwise, full marks may not be awarded even though the answer is numerically correct.
Note: This examination consists of 7 questions on 4 pages. Marks
Q. No Time: 3 hours Value Earned
1.
Considering the new development in modern theodolites, such as Robotic Total Station (compared with the old optical mechanical theodolites, such as Wild T1A theodolite), explain 5 important points on how the skills required of surveyors in operating the old optical mechanical theodolites are modified in operating modern total station (stating in each point the skill in operating specific aspect of the old optical mechanical theodolites and how the skill required in doing the same with modern total station has changed).
10
2.
Leica Distomat DI1600 EDM equipment was calibrated over Surrey EDM six- point baseline in BC. The constant correction for the EDM is assumed to be equal to zero and the manufacturer’s stated accuracy is 3mm 2ppm. The published mark-to-mark baseline distances (p) and the calculated mark-to-mark distances corrected for meteorological conditions (m) are fitted by least squares adjustment to a linear regression p = C + Sm, where C is the EDM constant correction and S is the scale factor. The m and p values are based on all the possible combinations of one-way distances among the baseline points. The following least squares adjusted quantities were obtained: 1-S = -3.01 ppm; ˆS= 1.05 ppm; C = 0.70 mm;
ˆC= 0.77 mm. Answer the following:
a) Test if ˆS is compatible with the manufacturer’s claimed scale factor error at 95% confidence level.
b) Test if the scale factor correction (1-S) is significantly different from zero at 95% confidence level.
6 5
3.
A survey contract requires determining local benchmark elevations following First Order procedure with the discrepancy between independent forward and backward levellings not exceeding 4 mm L at 99% confidence level (with L in
kilometres). A height difference is the average of the forward and backward levellings. Answer the following.
a) Derive an expression, based on the discrepancy and as a function of L, for the standard deviation of a height difference.
b) Using modern total stations [angular accuracy of 1 and a distance accuracy of 1 mm 1 ppm according to ISO Standards] has the potential for
competing with traditional differential levelling. Assuming the total station is used in a trigonometric levelling procedure with imposed sight length (60 m) and balanced sight length (within 10 m) limitations of First Order levelling procedure, determine numerically (stating any assumptions made) whether the levelling result will satisfy the First Order specification. [Let the average slope of the terrain (covered with the same material) be +1.5.]
c) Discuss five important advantages of trigonometric levelling over the traditional precise differential levelling.
5
15
5
Exam C-3 Advanced Surveying 2017 10 2 of 4 4.
The two commonly used methods of precise azimuth determination are based on the use of Global Navigation Satellite System (GNSS) and gyrotheodolite/gyro station equipment. Answer the following:
a) Discuss briefly (providing the purpose and how often it should be done in each method) an important field calibration process that may be required prior to field observation.
b) Discuss the sources of errors (systematic and random) in the azimuth determination in both methods and how they are minimized (providing 5 sources of errors for each method).
c) What steps and corrections are required in each method to transform the determined azimuths to grid azimuths?
6
10 4
5.
a) According to Donahue and others in their Guidelines for RTK/RTN GNSS Surveying in Canada, “working with a public or private Real-Time Network (RTN) can be a very precise and efficient way to perform cadastral and
engineering surveys.” What is RTN? How is it different from RTK? Discuss the issues (including how to solve them) that the surveyors must address a priori in preparation for RTN surveys.
b) As part of GNSS job specifications for a GNSS survey project, a fixed baseline of approximately 16,697 m in length (between control points A and B) was observed using static surveying procedures with specified accuracy of 5 mm + 1 ppm. The differences between the observed and fixed baseline components are 0.0074 m, 0.0013 m, 0.0050 m respectively for X, Y, Z components. If the setup error of 0.0015 m is assumed for each receiver, determine if the surveying procedures are acceptable at 95% confidence level.
c) A new point is tied to the geodetic control point A in (b) using the same static surveying procedures. If the new point is 5 km away from the control point A whose published network accuracy is 0.030 m, determine the local accuracy and the network accuracy for the new point.
8
4
3
6.
Answer the following with regards to deformation monitoring and analysis.
a) What is the observation differencing approach? Explain the conditions under which this approach may be used and discuss two disadvantages of the approach.
b) Discuss the important limitations in using terrestrial laser scanners in deformation monitoring surveys.
6 2
7.
a) In a tunneling survey, it is required of the vertical control network that the maximum relative vertical positional errors between any survey points along the tunnel be within a tolerance of 5 mm. Interpret this tolerance and calculate the expected standard deviation of any survey point in the network, clearly stating your assumptions. Suggest the appropriate Canadian vertical control levelling order for this project, assuming the longest distance between any two points is 2.8 km.
b) In the pre-analysis of a surface vertical network for a tunneling survey, describe how to determine error contribution, to the breakthrough error, due only to the proposed surface measurements.
7
4
100
Exam C-3 Advanced Surveying 2017 10 3 of 4
Some potentially useful formulae are given as follows:
2
360
ZI ZII
v
2 360 II
I Z
z Z
2
) 180 (
) sin(
HzI HzII z
c
2
) 180 (
) sin(
) tan(
HzI HzII z
c z
t
Corrected direction = Measured direction –
"2 tan NR NL v
z
v '
i z z or iv icos; iT HzHz' or
z iT i
tan sin
21 1
2 2 2 1 2
1 1
n i i
n n
i i
X n i
i i i
X X
Y Y
l l 2 1
1
2 2 1 1 2 21 1
n i i
n n
i i
X i i
i i i
X X
Y Y
l l
21 1
2 2 2 1 2
1 1
n i i
n n
i i
Y n i
i i i
Y Y
X X
l l 2 1
1
2 2 1 1 2 21 1
n i i
n n
i i
Y i i
i i i
Y Y
X X
l lDeformation: l2 l1 V Ad; d xˆ2xˆ1
d p
d d T
c F u df
u d Q
F d , ,
ˆ ˆ ˆ
2 0 0
1
ˆ
;
1 ˆ 2 0
ˆ ˆ
ˆ
T c d
d
d Q d
F u
< 0
2 ,df ud
ud
EDM:
273.16
1013.25 16 . 273 1 1t p na ng
(for p in mb and t in C)
106
) 1 (
n
N '(NREF Na)d'106
Standard pressure: 760 mmHg or 1013.25 mb; 0C or 273.15 K
1 2 3 4
( ... )
ˆ 1
M m m m m mn
C n
Levelling: 3mm L 4mm L 8mm L 24mm L 120mm L Statistics:
2 , df
z/2 tdf,/2
2
ˆ ,df
df
Exam C-3 Advanced Surveying 2017 10 4 of 4
Table 1: Normal Distribution table (upper tail area):
0.001 0.002 0.003 0.004 0.005 0.01 0.025 0.05 0.10 z 3.09 2.88 2.75 2.65 2.58 2.33 1.96 1.64 1.28 Table 2: Chi-Square Distribution table (lower tail area)
0.025 0.05 0.10 0.90 0.95 0.975 0.99 0.995
Degrees of freedom
1 0.001 0.004 0.016 2.705 3.841 5.024 6.635 7.879 2 0.051 0.103 0.211 4.605 5.991 7.378 9.210 10.597 3 0.216 0.352 0.584 6.251 7.815 9.348 11.345 12.838 11 3.816 4.575 5.578 17.275 19.675 21.920 24.725 26.757 12 4.404 5.226 6.304 18.549 21.026 23.337 26.217 28.300 13 5.009 5.892 7.041 19.811 22.362 24.736 27.688 29.819 14 5.629 6.571 7.790 21.064 23.685 26.119 29.141 31.319 15 6.262 7.261 8.547 22.307 24.996 27.488 30.578 32.801
Table 3: Table for Student-t distribution ( is upper tail area) t
Degree of freedom t 0.10 t 0.05 t 0.025 t 0.01
1 2
3.08 6.31 12.7 31.8
1.89 2.92 4.30 6.96
3 1.64 2.35 3.18 4.54
4 1.53 2.13 2.78 3.75
5 1.48 2.01 2.57 3.36
6 1.49 1.94 2.45 3.14
11 1.363 1.796 2.201 2.718
12 1.356 1.782 2.179 2.681
13 1.350 1.771 2.160 2.650
14 1.345 1.761 2.145 2.624
15 1.341 1.753 2.131 2.602
